Geodesic
Analysis of the linearly implicit mid-point rule for differential- algebraic equations
Electronic transactions on numerical analysis, Tome 1 (1993), pp. 1-10
The error of the linearly implicit mid-point rule after 2m + 1 steps is expanded in powers of m2. We prove that the well-known expansion for ordinary differential equations (an expansion in negative powers of m2) is perturbed by additional terms with non-negative powers of m2 for semi-explicit differential-algebraic equations of index one. Hence, extrapolation in m - 2 will be of limited value only. The complete expansion shows these limits and, furthermore, can be used to derive an order 8 method of Rosenbrock type.
Classification : 65L05, 65B05, 58F99
Keywords: differential-algebraic equations, linearly implicit mid-point rule, rosenbrock-type methods, extrapolation 
@article{ETNA_1993__1__a6,
     author = {Schneider,  Claus},
     title = {Analysis of the linearly implicit mid-point rule for differential- algebraic equations},
     journal = {Electronic transactions on numerical analysis},
     pages = {1--10},
     year = {1993},
     volume = {1},
     zbl = {0809.65083},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_1993__1__a6/}
}
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Schneider,  Claus. Analysis of the linearly implicit mid-point rule for differential- algebraic equations. Electronic transactions on numerical analysis, Tome 1 (1993), pp. 1-10. http://geodesic.mathdoc.fr/item/ETNA_1993__1__a6/